I'm quite sure he wants $2M more per year, not over the course of five seasons. By all accounts, he wants $12M annually and is seeing offers closer to $10M. It's important for teams to have a line they've drawn that they will not cross, because at that point it's a bad deal. Maybe the Patriots' number is somewhere over their initial offer, but they will not cross their line, even if it is by $5. All of the the player's potential risk:reward is built into that number, including the player's locker room presence, knack for big plays, fit in their system, etc. So, the Patriots have a number, below which is considered a positive value transaction and above which is considered a negative value transaction. They've let many players walk because they wouldn't go up just a little more, such as a million or two per year.
The Jets have apparently offered him "far and away" the most money, according to that La Confora article a few posts above. The on-field product speaks for itself between these two franchises. I guess they didn't learn from the Darrelle Revis fiasco that you don't go all-in at all costs in order to land a big-named player because instead of weakening your rival, you yourself will be weaker against them. The even better part is Hightower will be misused with the Jets, so it makes their offer even dumber. Then again, they are the dumbest organization in the league.